A small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the first column, second column, and third column respectively. Use the constant terms in the last column. Also remember to use O for the missing coefficient of a variable. 1 :292,500 1 .09 .10 .12 : 29,900 -1

A small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the first column, second column, and third column respectively. Use the constant terms in the last column. Also remember to use O for the missing coefficient of a variable. 1 :292,500 1 .09 .10 .12 : 29,900 -1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Write the system of equations as an augmented matrix -5y7b = -24 -7y -26 6b 00

Q: small software corporation borrowed $320,000 to expand its software line. The corporation borrowed…

A: Given, A small software corporation borrowed $320,000 to expand its software line. The corporation…

Q: Solve the following system of equations by using row operations on matrices. 10х - 6y = 42 7x+2y= 16

A: The given system of equations is 10x - 6y = 42 . . . . . . . . . . (1) 7x + 2y = 16…

Q: A young superhero mixes up a batch of goo they can use to fight crime. The recipe for the goo…

A: W be the amount of water C be the amount of cola A be the amount of alcohol

Q: Solve the following system of linear equations using matrix inversion. 1- y+ 6z = 8 I+: = 5 I+ 3y -…

Q: Write the following system of equations in matrix form: AX-C a. 3xay+2z-5 b. 2x+y-22-2 c. Xy+3z-0

A: Let's find.

Q: A small software corporation borrowed $380,000 to expand its software line. The corporation borrowed…

Q: A standard rectangular highway billboard has a perimeter of 124 ft. The length is 34 ft more than…

A: Solution

Q: Use matrices to solve the following system: 4a-2b-3c+d = 3 2a-2b-5c = -10 4a+b+2c+d=17 3a+c+d = 12

Q: If his total revenue from a day's

A: We have to find out the number of cakes he produces in a day. It is given that plum cake cost is…

Q: Express the situation as a system of two equations in two variables. Be sure to state clearly the…

A: Solution: Let us assume that; The number of TV ads are x and the number of radio ads are y.

Q: Robyn owns and operates two souvenir shops. At his Sabina Park shop, sweatshirts cost $4500 and…

A: Given that Robyn owns and operates two souvenir shops. At his Sabina Park shop,sweatshirts cost…

Q: A person invested $7600 for 1 year, part at 8%, part at 9%, and the remainder at 14%. The total…

A: Total money invested = 7600let x be amount invested at 8%y be the amount invested at 9%z be the…

Q: Solve the following system of equations by using row operations on matrices. 18x + 6y = 2 12x - 24y…

A: Consider the system of equations

Q: Mr. Adams wants to rent a beachfront condominium. Unit 1 costs $1,200 for the week plus a cleaning…

A: Unit 1 $1200/week and( $ 50/day cleaning) Unit 2 $1450/week and no cleaning fees.

Q: Write a system of equations for the following situations and solve using inverse matrices. 4. A…

A: Let she made x numbers of 3-point field goals Let she made y numbers of 2-point field goals Let she…

Q: Solve the following system of equations by hand, using either the tabulation method or the matrix…

Q: A chemical plant produces products D, E, F, and G. There are twice as many D as E produced on a…

A: There are twice as many D as E produced on a daily basis. 2D=E 2D-E=0…

Q: two students in the same Spanish class, Tristan and Nancy, plan to get together after school to make…

Question

A small software corporation borrowed $292,500 to expand its software line. Some of the money was
borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was
borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the
amount borrowed at 9%. Solve the system using matrices.
Step 1
Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12%
be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed
at 10% was 2- times the amount borrowed at 9%.
Write a set of equations using the information given. Convert the percentage to decimal fraction.
x + y + z = 292,500
.09
x +.10
y + |.12
V z = 29,900
X x - y = 0
Write the associated augmented matrix for the given system of equations.
Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients
of x, y and z as entries of the first column, second column, and third column respectively. Use the constant
terms in the last column. Also remember to use O for the missing coefficient of a variable.
1
:292,500
1
.09
.10
.12
: 29,900
-1

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Systems of Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

On Monday, Sarah picked up lunches for her friends and spent $17.30 on 3 tofu banh mi and 2 bubble teas. On Friday she spent $26.75 on 5 tofu banh mi and 3 bubble teas. Set up a system of two linear equations to represent this situation, then write down the associated augmented matrix for this system. Do not solve this system.
A small software corporation borrowed $315,000 to expand its software line. The corporation borrowed some of the money at 3%, some at 4%, and some at 5%. Use a system of equations to determine how much was borrowed at each rate when the annual interest was $13,500 and the amount borrowed at 4% was 22/12/2012 times the amount borrowed at 3%. Solve the system using matrices. amount borrowed at 3% $ amount borrowed at 4% $ amount borrowed at 5% $
Write the following system of equations as a single matrix equation. 5z -9x = 0 5y = -4+ 6z 8x +7y-10 = 0 Answer 72021 Hawkes Learning
Solve this application problem using a system of equations: A grocery store recently sold a bag of peanuts for $0.76 and a bag of pistachios for $3.68. At the end of that day, 50 bags of peanuts and pistachios were sold for a total of $128.52. How many bags of each were sold?
A Sillall software corporation borrowed $115,000 to expand its software line. The corporation borrowed some of the money at 3%, some at 4%, and some at 5%. Use a system of equations to determine how much was borrowed at each rate when the annual interest was $5,300 and the amount borrowed at 4% was times the amount borrowed at 3%. Solve the system using matrices. amount borrowed at 3% amount borrowed at 4% $ amount borrowed at 5% Need Help? Master It Read It Submit Answer
A group of three friends have 3 different jobs. Mallory(m) makes $9 an hour at Kroger, Chandler(c) makes $11 at HEB, and Sophia(s) makes $8 at Cinemark. All together they worked a total of 40 hours and earned $370. Mallory worked twice as many hours as Chandler. How many hours did each friend work?
What volume of each of a 5% acid solution and a 65% acid solution should be combined to form 46 ml of a 50% solution? Set up the appropriate equations and solve the system using the inverse of the coefficient matrix. Combine O ml of the 5% acid solution withO mL of the 65% acid solution to form 46 mL of a 50% solution. (Type integers or decimals. Round the final answers to two decimal places as needed. Round all intermediate values to two decimal places as needed.)